Computer multimedia applications typically involve the processing of high volumes of data values representing audio signals and video images. Processing the multimedia data often includes performing transform coding which is a method of converting the data values into a series of transform coefficients for more efficient transmission, computation, encoding, compression, or other processing algorithms.
More specifically, the multimedia data values often represent a signal as a function of time. Transform coefficients represent the same signal as a function, for example, of frequency. There are numerous transform algorithms, including the fast Fourier transform (FFT), the discrete cosine transform (DCT), and the Z transform. Corresponding inverse transform algorithms, such as an inverse discrete cosine transform (iDCT), convert transform coefficients to sample data values. Many of these algorithms include multiple mathematical steps that involve decimal numbers.
In an effort to allow for easy interchange of graphical formats, the International Standards Organization (ISO) and the Consultative Committee for International Telegraph and Telephone (CCITT) formed the Joint Photographic Experts Group (JPEG) and the Moving Pictures Expert Group (MPEG). The JPEG/MPEG committee published compression standards that use the Discrete Cosine Transform (DCT) algorithm to convert a graphics image to the frequency domain. Efficient implementations of the DCT algorithm is an interest since JPEG and MPEG algorithms strive to achieve real-time performance. Most multimedia development software that uses this type of compression depend on the use of a coprocessor to generate compression.
DCT is widely used in one dimensional (1D) and two dimensional (2D) signal processing. 2D 8×8 DCT is the basis for JPEG and MPEG compression. While there are presently algorithms that directly compute 2D 8×8 DCT, taking the 8-point 1D transform of the rows and the columns is equivalent to the 2D 8×8 transform. There exists algorithms that compute 1D 8-point DCT which can be used in the row-column method to perform a 2D 8×8 DCT.